Friday, June 1, 2012

Commutative Algebra 2nd ed. - H. Matsumura

Commutative Algebra
This book, based on the author's lectures at Brandeis University in 1967 and
1968, is designed for use as a textbook on commutative algebra by students of
modern algebraic geometry or abstract algebra.
Part I is devoted to basic concepts such as dimension, depth, normal rings, and
regular local rings; Part II deals with the finer structure theory of noetherian
rings initiated by Zariski and developed by Nagata and Grothendieck.
In this second edition, the chapter on Depth has been completely rewritten.

There is also a new Appendix consisting of several sections, which are almost
independent of each other. The Appendix has two purposes: to prove the
theorems used but not proved in the text; to record same of the recent
achievements in the areas connected with Part II.
For specialists in commutative algebra, this book will serve as an introduction
to the more difficult and detailed books of Nagata and Grothendieck.
To geometers, it will be a convenient handbook of algebra.
Review of the First Edition:
"This is an excellent book which :ontains a wealth of material... Part I, for
which the prerequisites are rain imal, develops the main concepts, central'to
modern commutative algebra... Part II, is considerably more advanced../'
- American Mathematical Monthly

Hideyuki Matsumura, Professor of Mathematics at Nagoya University, received his graduate training at Kyoto University and was awarded his Ph.D. in 1959. Formerly Associate Professor of Mathematics at this university, Professor Matsum,u. ra was_a<.  . research associate at the UniverSity of Pisa during 1962 and 1963. He was also Visiting Associate Professor at the University of Chicago (1962), at Johns Hopkins University (1963), at Columbia University (1966-1967), and at Brandeis University (1967-1968). The author spent 1973 and 1974 as Visiting Professor at the University of Pennsylvania, 1974 and 1975 as Visiting Professor at the Politecnic of Torino, and 1977 as Visiting Professor at the University of MOnster.